As a matter of fact, things exist. But suppose I try to think the counterfactual state of affairs of there being nothing, nothing at all. Can I succeed in thinking pure nothingness? Is this thought thinkable? Is it thinkable that there be nothing at all? And if it is, does it show that it is possible that there be nothing at all? Could there have been nothing at all? If yes, then (i) it is contingent that anything exists, and (ii) everything that exists exists contingently, which respectively imply that both of the following are false:
1. Necessarily, something exists: □(∃x)(x exists).
2. Something necessarily exists: (∃x)□(x exists).
(1) and (2) are not the same proposition: (2) entails (1) but not conversely. If you confuse them you will be justly taxed with an operator shift fallacy.
Phylogenetically, this topic goes back to Parmenides of Elea. Ontogenetically, it goes back to what was probably my first philosophical thought when I was about eight or so years old. (Ontogeny recapitulates phylogeny!) I had been taught that God created everything distinct from himself. One day, lying in bed and staring at the ceiling, I thought: "Well, suppose God never created anything. Then only God would exist. And if God didn't exist, then there would be nothing at all." At this thought my head began to swim and I felt a strange wonder that I cannot quite recapture, although the memory remains strong decades later. The unutterably strange thought that there might never have been anything at all — is this thought truly thinkable or does it cancel itself in the very attempt to think it?
I am torn between two positions. On the one it is provable that necessarily something exists. On the other, it is not provable.
Here is one sort of argument for the thesis that necessarily something exists and that it is therefore impossible that there be nothing at all. The argument has the form of a reductio ad absurdum.
1. There are no propositions. (Assumption for reductio)
2. (1) is either true or false.
3. Whatever is either true or false is a proposition. (This is by definition. Propositions are truth-bearers or vehicles of the truth-values. They are whatever it is that is appropriately characterizable as either true or false.)
Therefore
4. If (1) is true, then there is at least one proposition. (2, 3)
But equally
5. If (1) is false, then there is at least one proposition. (2, 3)
Therefore
6. Necessarily, there is at least one proposition.
Therefore
7. (1) is necessarily false.
Therefore
8. It is not possible that nothing exists. Necessarily, at least one proposition exists.
Skeptical Rejoinder
I don't buy it. Had there been nothing at all, there would not have been any propositions, any states of affairs, any way things are, any properties, any truth, any Law of Non-Contradiction or Law of Excluded Middle or Principle of Bivalence, any distinction between true and false, any distinctions at all. There would have been just nothing at all. Your proof that this is impossible begs the question by assuming or presupposing the whole interconnected framework of propositions, truth and falsehood, etc., including your modal principles and other logical principles.
You can't prove that there must be something if you presuppose that there must be something. Circular arguments are of course valid, but no circular argument is a proof.
At the very most, what you demonstrate is that WE cannot operate without presupposing the Logical Framework — to give it a name. At the very most, you demonstrate that the Logical Framework (LF) is a transcendental presupposition of OUR discursive activities, in roughly the Kantian sense of 'transcendental.' You do not succeed in demonstrating that Being itself or any being exists independently of us. Your proof may have transcendental import, but it fails to secure ontological import. Why do you think that Being itself, independently of us, is such that necessarily something exists?
You think that there must be a total way things are such that, if there were nothing at all, then that would be the way things are, in which case there would, in the end, be a way things are. But how do you know that? How do you know that your presupposition of a way things are is more than a merely transcendental presupposition as opposed to a structure grounded in the very Being of things independently of us?
I grant you that the LF is necessary, but its necessity is conditional: it depends on us, and we might not have existed. For all you have shown, there could have been nothing at all.
Why does it matter? What's at stake?
Now this is a highly abstract and abstruse debate. Does it matter practically or 'existentially'?
If there could have been nothing at all, then all is contingent and no Absolute exists. An Absolute such as God must be a necessary being. An Absolute functions as the real-ground of the existence, intelligibility, and value of everything distinct from it. If there is no Absolute, then existence is absurd, i.e., without ultimate ground (source and reason), without sense and intelligibility. Now if existence is absurd, then human existence is absurd. So if there could have been nothing at all, then human existence is absurd. This is why our question matters. It matters because it matters whether our existence is absurd.
Coda
I am left with the thought that is reasonable to hold that there must be something — after all I argued the matter out rigorously — but also reasonable to hold the opposite. This seems to suggest that here we have a question that discursive reason cannot decide. So how do we decide it? By personal decision? By mystical intuition? By acceptance of divine revelation? In some other way? In no way?